When you look hard enough, there's always options how it might happen.
Oxygen is something that is required by a lot of organisms. Plants create oxygen, but expell the surplus they don't need into the air. So we can establish that positive products that can be used as energy can be expelled by such organisms. Potentially electricity as well.
Another example is plankton or algea producing bioluminescence. Search for bioluminescent waves and see some beautiful examples. When these organisms are moved they can produce this light. It's thought to be a way to deter or confuse predators, but there is no certainty yet as far as I can see.
The title suggests organism, the question suggests creature and the description seems to want a larger creature that can produce a steady current. Although it might be possible, it's more likely that it'll be a large group of tiny creatures/plants producing the electric fields. They can do this as a surplus product or attack/defence mechanism. Either way, the large amount of tiny organisms can produce a steady electric field together, as the electric pulses should even out most of the time thanks to the large numbers. The plants can react and much like the creatures reacted to the huge influx of oxygen in the old days. Adapt to the new environment and start using the electric fields as a supplement energy. This can in turn be beneficial to the electricity producing organisms, which likely feed on the plants and use it for shelter.
Keep in kind that there are ways in nature that aren't organic to produce energy. There's crystals that produce energy/electricity when stresses are applied, or when photons hit them. There even used to be naturally occurring nuclear reactors on Earth. Electric culture has a chance of naturally occurring. Do keep in mind that as far as I can see it hasn't happened yet, so the chances it happening naturally are either unlikely, simply haven't occured yet by chance, difficult to spot or impossible but we don't know it yet.